What is the ruling on publishing "stories" - pictures or videos - a period of time after they were taken, with the current time added, which might suggest to the viewer that they were taken and updated live? Is this considered a lie, and does the ruling depend on the publisher's intention?

Explicit writing carries the same ruling as speech. Therefore, placing the current time on pictures that have an earlier date is like saying that with the tongue, and thus it is considered a lie. As for merely arranging pictures in a way that implies a different date without explicit writing, such as placing daytime pictures during the day and nighttime pictures at night, this is more akin to tawriyah (equivocation) and ta'rid (allusion). Its ruling depends on its purpose and what results from it.